Symmetrized density-matrix renormalization-group method for excited states of Hubbard models

We extend the density-matrix renormalization-group (DMRG) method to exploit parity, ${\mathit{C}}_2$ (rotation by π), and electron-hole symmetries of model Hamiltonians. We demonstrate the power of this method by obtaining the lowest-energy states in all eight symmetry subspaces of Hubbard chains with up to 50 sites. The ground-state energy, optical gap, and spin gap of regular U=4t and U=6t Hubbard chains agree very well with exact results. This development extends the scope of the DMRG method and allows future applications to study of optical properties of low-dimensional conjugated polymeric systems. © 1996 The American Physical Society.